Sand is good in small amounts with a soil mix and desert sands CAN be good, as their calcium-rich alkalinity can sweeten carrot flavor, but if those sands are too salty, most vegetables don't like soils with too much free sodium. Rinsed sands are one way to avoid this, you can wash out some sodium chlorides & carbonates while keeping the calcium & manganese oxides. I have to admit I have no idea about the particulars of Dubai desert sand and am generalizing based on California's desert sands. Sounds like what you need is fully composted organic matter - grass, leaves, bark, manure, ... Sand has essentially no nitrogen and purchased soil often lacks the useful microrganisms that help process dead vegetation into usable nutrients anyway. Some mall soils are mainly useful as a way of maintaining drainage in containers and preventing root rot, but if they are all you use, it's like putting your crops on a diet. That's why so many people add chemical fertilizers to container plants. But you want to try and avoid bringing in diseases or pests along with the compost, there's always some risk with non-sterile soil amendments. It's a bit of a balancing act as well as the subject of quite a lot of discussion about creating perfect soil mixes for particular plants. As a novice, you mainly want to understand that you must have nitrogen to even get the plants growing, then phosphorus and potassium (N/P/K on fertilizer labels) and micro-nutrients for crop production. Desert sands will almost guarantee you potassium and if you want to extend your gardening knowledge into ecological knowledge about your surroundings, using various native soils in your yard can be very educational.

The carrot is a hardy, cool season crop that can be planted in the garden as soon as the soil can be prepared in the spring. Carrots require relatively large amounts of moisture and are not tolerant of drought. Prolonged hot weather in the later stages of development may not only retard growth but result in an undesirable strong flavor and coarseness in the roots. At the other extreme, prolonged temperatures below 55 degrees F tend to make the roots longer, more slender and paler in color than expected. The best temperature for highest quality roots is between 60 and 70 degrees F Here is a link that might be useful: More on carrots

Early use of the garden weasel followed by a grass-clipping mulch are keeping the weeds down nicely. The mulch retains water. Anything I were to grow in the narrow spaces between the plants would require watering instead. Zone and geology make a great deal of difference. Gardening in Massachusetts on a sand that was unsorted glacial till gave me little trouble -- except that I mulched for the first time (mulch plus soggy clay in a steamy, Western PA summer would have been a sure recipe for fungal diseases). The Carolina Sandhills are the remains of an ancient beachfront. The sand is nearly pure quartz and the grains are almost all the same size so its quite different from my Massachusetts sand. And the blistering days (I never thought I'd ever utter the phrase "Its not too hot today. Its only 90.), suck the moisture away so rapidly that I water only at the plants' roots. Any weed seeds in the area that I did not mulch yet are not sprouting because it hasn't rained in 3 weeks. My neighbor uses an annual rye grass on his garden over the winter with good results, but he doesn't care if his garden gives him nothing between late October and mid-June since he only grows beans, tomatoes, peppers, eggplant, and cucumbers. :-)

Are you growing it for seed? Then cover the red all the way with soil. The plant probably needs less water, more sun. I do that with all root vegs to get seed the same season. Cut about an inch below the top, eat the bottom part, replant the top. It will seed the same season. If you are trying to grow the root part again to get another carrot out of it, I don't think that works. All you will get is hairy rootlets growing from the edge of the carrot.